Quantized semiconductor structures are presently under investigation for their physical properties and their potential for device applications. The theoretical modeling of these structures is particularly important for complementing fabrication technology due to the predictive capabilities of device modeling and its ability to guide the design process. This thesis investigates novel electronic and transport properties of quantized devices and develops various methods for their simulation. Both the dissipative and coherent regimes of quantum transport are considered.A three-dimensional self-consistent Schrodinger-Poisson simulation is used to investigate a single-electron tunneling structure operating under linear response conditions. The device considered contains multiple regions of quantum dimensionality which are comprehensively treated in the self-consistent solver. Coherent transport characteristics are evaluated using an interacting form of the Landauer formula. The model incorporates exchange-correlation effects and implicitly accounts for the Coulomb blockade of resonant tunneling. The theoretical transport characteristics of the structure exhibit the same general oscillatory properties as the experimental data and point to the prominence of interface disorder in establishing conductance amplitudes.Transport characteristics under dissipative conditions are evaluated using a Monte Carlo calculation tailored to quantized structures. A quantum wire serves as the model device and the influence of polar optical phonon (POP) scattering is examined for various biasing and confinement topologies. Several novel effects associated with resonant intersubband optical phonon scattering are revealed including intersubband population inversions and negative differential transconductances. Experimental observation of the latter effect has been confirmed through self-consistent determination of the electronic spectrum in the experimental device. Finally, an investigation is made of low-temperature spatial velocity oscillations due to quasi-coherent POP emission.